The graph above shows the proportions of 9 material categories

Question

https://gmatclub.com/gmat-focus-tests/resources/import/img/I10-20.png The graph above shows the proportions of 9 material categories comprising 254 million tons of municipal solid waste in 2013 before potential recycling. Select from each drop-down menu the option that creates the most accurate statement based on the information provided. If 50% of paper waste and 35% of metal waste were recycled in 2013, then the amount of recycled paper, in tons, would be approximately GRAPH_1_PLACEHOLDER times that of recycled metal waste. If the weight of plastic waste remained the same in 2014 while the weight of total waste increased by 10% from 2013 to 2014, and the increase in tons was evenly distributed across the other eight categories, then a GRAPH_2_PLACEHOLDER increase would represent the greatest percent increase in tons of waste for any of the eight categories from 2013 to 2014. 6.jpg

Bunuel · Answer

Drop-down 1: 
 
Paper waste contributes 27% of the total waste. Since 50% of that was recycled, 13.5% of paper waste was recycled. Metal waste contributes 9.1% of the total waste. Since 35% of that was recycled, approximately 3.2% of metal waste was recycled. Therefore, the amount of recycled paper was approximately  \frac{13.5}{3.2} \approx 4.2  times that of recycled metal waste.
 
 Drop-down 1: 
 
The total waste increased by 10% from 2013 to 2014, accounting for a 25.4 million ton increase in total waste. Since this increase was evenly distributed across the eight categories, each category increased by  \frac{25.4}{8} \approx 3.2  million tons of waste. The addition of 3.2 million tons would result in the greatest percentage increase for the waste category with the least waste in 2013. That category was Glass, which accounted for 3.3% of 254 million tons, approximately 8.4 million tons. The increase of 3.2 million tons would constitute an increase of  \frac{3.2}{8.4} * 100 \approx 38\% .

Correct answer:

Dropdown 1:  "4"

Dropdown 2:  "38%"

Bismuth83 · Answer

1. The amount of recycled paper waste would be equal to  50\% * 27\% * 254 = 34.29  million tons and the amount of recycled metal waste would be equal to  35\% * 9.1\% * 254 = 8.0899  million tons. The ratio is equal to  \frac{34.29}{8.0899} \approx 4.24 , which is closest to 4.

2. A 10% increase distributed over 8 categories is the same as  10\% * 254 * \frac{1}{8} = 3.175  million tons being distributed to each category apart from plastic waste. This would be the greatest percent increase for the category with the smallest amount - glass, which would go from  3.3\% * 254 = 8.382  to  8.382 + 3.175 = 11.557  million tons. This is a  \frac{3.175}{8.382} * 100\% \approx 37.88\% , which is closest to 38%.

3. Our answer will be:   4 and 38%  .

pappal · Answer

1. 0.5 of paper waste = k times 0.35 of metal waste
 0.5*0.27*254=k*0.35*0.09*254
k=0.5*0.27/0.35*0.09 ~  4 times 
2. total waste increases by 10% i.e. 25.4 ton which is evenly distributed among all other 8 categories than plastic waste.
hence all the values in the other categories increase by 25.4/8=3.2 ton
now since lowest value of the waste is of glass i.e. 3.3% so will have the greatest %age increase
which is 3.2/3.3*2.54 slightly less than 40%~~ 38%

odionam · Answer

in 2nd part 10% increase redistributed in other 8 can't we do it without conversion like 10%/8= 1.25% in crease in othrer 8 glass is least so gratetest it increase so 1.25/3.3 =approx 38%

egmat · Answer

Hi odionam,

Yes, your shortcut is completely valid, and it lands on  38%  for exactly the right reason. You do not need to convert anything to tons.

Here is why it works. Every number in this problem is a share of the  same  base: the 2013 total of  254  million tons. The pie slices are percentages of it, and the  10%  increase is measured against it too. So when you divide one by the other, the  254  cancels out and never has to appear.

- Added to each category =  10%  of the total /  8  =  1.25%  of the total
- Glass in 2013 =  3.3%  of the total - the thin orange sliver on the chart, and still the smallest of the eight once plastics ( 12.8% ) is set aside
- Percent increase for glass =  1.25  /  3.3  = approximately  0.379 , so  38%

Bunuel's  3.175  /  8.382  is that identical fraction with  254  multiplied back into the top and the bottom. Same ratio, more arithmetic.

When this shortcut would break

Only if the two percentages sat on different bases. Round-number check: total  100 , a  10%  increase =  10 , split over  4  categories =  2.5  each; the smallest category at  5%  of  100  =  5 , so its increase is  2.5  /  5  =  50%  - and ( 10  /  4 ) /  5  gives  50%  too. If instead the  10%  had been measured on the  2014  total, the bases would no longer match and you would have to convert first.

Answer: 38%  (Dropdown 2; Dropdown 1 is  4 )

The graph above shows the proportions of 9 material categories

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The graph above shows the proportions of 9 material categories

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